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A Power Schur Complement Low-Rank Correction Preconditioner for General Sparse Linear Systems

A parallel preconditioner is proposed for general large sparse linear systems that combines a power series expansion method with low-rank correction techniques. To enhance convergence, a power series expansion is added to a basic Schur complement iterative scheme by exploiting a standard matrix splitting of the Schur complement. One of the goals of the power series approach is to improve the eigenvalue separation of the preconditioner thus allowing an effective application of a low-rank correction technique. Experiments indicate that this combination can be quite robust when solving highly indefinite linear systems. The preconditioner exploits a domain-decomposition approach, and its construction starts with the use of a graph partitioner to reorder the original coefficient matrix. In this framework, unknowns corresponding to interface variables are obtained by solving a linear system whose coefficient matrix is the Schur complement. Unknowns associated with the interior variables are obtained by solving a block diagonal linear system where parallelism can be easily exploited. Numerical examples are provided to illustrate the effectiveness of the proposed preconditioner, with an emphasis on highlighting its robustness properties in the indefinite case.

Ketersediaan

Informasi Detail

Judul Seri

SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS; Vol.42 No.2 April-June 2021

No. Panggil

-

Penerbit

: .,

Deskripsi Fisik

p. 659 - 682

Bahasa

English

ISBN/ISSN

-

Klasifikasi

-

Tipe Isi

-

Tipe Media

-

Tipe Pembawa

-

Edisi

-

Subjek

KRYLOV SUBSPACE METHOD
DOMAIN DECOMPOSITION
SCHUR COMPLEMENT
PARALLEL PRECONDITIONER
LOW-RANK CORRECTION
POWER SERIES EXPANSION

Info Detail Spesifik

https://doi.org/10.1137/20M1316445

Pernyataan Tanggungjawab

Qingqing Zheng, Yuanzhe Xi, Yousef Saad

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